Exploiting Configurational Freezing in Nonequilibrium Monte Carlo Simulations

Nicolini, Paolo; Frezzato, Diego; Chelli, Riccardo

doi:10.1021/ct100568n

Cited by 36 publications

(79 citation statements)

References 54 publications

(93 reference statements)

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“…The exponential nature of the Boltzmann weights makes the average in

normalΔ {\overset{false^}{F}}_{J}

notoriously difficult to converge because it is dominated by typically poorly sampled negative work values, a problem that is exacerbated by large dispersion in the work values . Accordingly, many have developed methodologies that limit the dispersion of the nonequilibrium work values in the first place . Others have proposed corrections or block‐averaging, combinatorial averaging, and extrapolation analysis protocols that have proved useful in improving the exponential average in the finite sampling limit …”

Section: Introductionmentioning

confidence: 99%

On the accurate estimation of free energies using the jarzynski equality

et al. 2018

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The Jarzynski equality is one of the most widely celebrated and scrutinized nonequilibrium work theorems, relating free energy to the external work performed in nonequilibrium transitions. In practice, the required ensemble average of the Boltzmann weights of infinite nonequilibrium transitions is estimated as a finite sample average, resulting in the so‐called Jarzynski estimator, normalΔFfalse^J. Alternatively, the second‐order approximation of the Jarzynski equality, though seldom invoked, is exact for Gaussian distributions and gives rise to the Fluctuation‐Dissipation estimator normalΔFfalse^FD. Here we derive the parametric maximum‐likelihood estimator (MLE) of the free energy normalΔFfalse^ML considering unidirectional work distributions belonging to Gaussian or Gamma families, and compare this estimator to normalΔFfalse^J. We further consider bidirectional work distributions belonging to the same families, and compare the corresponding bidirectional normalΔFfalse^italicML∗ to the Bennett acceptance ratio (normalΔFfalse^BAR) estimator. We show that, for Gaussian unidirectional work distributions, normalΔFfalse^FD is in fact the parametric MLE of the free energy, and as such, the most efficient estimator for this statistical family. We observe that normalΔFfalse^ML and normalΔFfalse^italicML∗ perform better than normalΔFfalse^J and normalΔFfalse^BAR, for unidirectional and bidirectional distributions, respectively. These results illustrate that the characterization of the underlying work distribution permits an optimal use of the Jarzynski equality. © 2018 Wiley Periodicals, Inc.

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“…The exponential nature of the Boltzmann weights makes the average in

normalΔ {\overset{false^}{F}}_{J}

Section: Introductionmentioning

confidence: 99%

On the accurate estimation of free energies using the jarzynski equality

et al. 2018

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“…Many have characterized this bias in terms of parameters of the underlying work distribution; Kofke and co‐workers have proposed a heuristic to evaluate whether the free energy estimate is biased or not (Wu & Kofke, 2005, 2005); Zuckermann and colleagues have proposed extrapolation methods to correct for this bias (Bucher, Walker, & McCammon, ; Echeverria & Amzel, ; Ytreberg & Zuckerman, ; Zuckerman & Woolf, , ). Additionally, methods have been proposed to specifically limit the variance of the work distribution itself (Chelli, ; Nicolini, Frezzato, & Chelli, ; Ozer, Valeev, Quirk, & Hernandez, ; Ramírez, Zeida, Jara, Roitberg, & Martí, ; Schmiedl & Seifert, ; Vaikuntanathan & Jarzynski, ; Zerbetto, Piserchia, & Frezzato, ).…”

Section: Introductionmentioning

confidence: 99%

Lessons learned about steered molecular dynamics simulations and free energy calculations

et al. 2019

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The calculation of free energy profiles is central in understanding differential enzymatic activity, for instance, involving chemical reactions that require QM‐MM tools, ligand migration, and conformational rearrangements that can be modeled using classical potentials. The use of steered molecular dynamics (sMD) together with the Jarzynski equality is a popular approach in calculating free energy profiles. Here, we first briefly review the application of the Jarzynski equality to sMD simulations, then revisit the so‐called stiff‐spring approximation and the consequent expectation of Gaussian work distributions and, finally, reiterate the practical utility of the second‐order cumulant expansion, as it coincides with the parametric maximum‐likelihood estimator in this scenario. We illustrate this procedure using simulations of CO, both in aqueous solution and in a carbon nanotube as a model system for biologically relevant nanoheterogeneous environments. We conclude the use of the second‐order cumulant expansion permits the use of faster pulling velocities in sMD simulations, without introducing bias due to large dispersion in the non‐equilibrium work distribution.

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“…For a detailed comparison between non-equilibrium tools and conventional equilibrium strategies (e.g., smart Monte Carlo routes like the umbrella sampling) we address the interested reader to ref. 15 Going to more extended systems, applications of the JE can be found in problems like estimating free energies of solvation of solute molecules in given media (e.g., hydration of methane 16,17 ). Typical applications are encountered in biological contexts, e.g.…”

Section: Introductionmentioning

confidence: 99%

Towards bulk thermodynamics via non-equilibrium methods: gaseous methane as a case study

Zerbetto

Frezzato

2015

Phys. Chem. Chem. Phys.

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We illustrate how the Jarzynski equality (JE), which is the progenitor of non-equilibrium methods aimed at constructing free energy landscapes for molecular-sized fluctuating systems subjected to steered transformations, can be applied to derive equations of state for bulk systems. The key-step consists of physically framing the computational strategy of "total energy morphing", recently presented by us as an efficient implementation of the JE [M. Zerbetto, A. Piserchia, D. Frezzato, J. Comput. Chem., 2014, 35, 1865-1881], in terms of build-up of the real thermodynamic state of a bulk material from the corresponding ideal state, in which the particles are non-interacting. In this context, the JE machinery yields the excess free energy versus suitably chosen controlled state variables, whose thermodynamic derivatives eventually lead to the equation of state. As an explanatory case study, we apply the methodology to derive the equation of state of gaseous methane by constructing the Helmholtz free energy versus the particle density (at fixed temperature) and then evaluating the thermodynamic derivative with respect to the volume. In our intent, this "old-style" work on gaseous methane should open the way for the investigation of thermodynamics of extended systems via non-equilibrium methods.

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Exploiting Configurational Freezing in Nonequilibrium Monte Carlo Simulations

Cited by 36 publications

References 54 publications

On the accurate estimation of free energies using the jarzynski equality

On the accurate estimation of free energies using the jarzynski equality

Lessons learned about steered molecular dynamics simulations and free energy calculations

Towards bulk thermodynamics via non-equilibrium methods: gaseous methane as a case study

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